/math/ - Mathematics

this but axiom of choice is also bullshit

I bought once some English chips which turned out to be a package of packages in chips. Does it mean I can duplicate chips?

I think the validity of the use of the real numbers depends on whether space is continuous or discrete, or whatever it is. I don't know of a way to prove either or. But definitely the popular notation of Writing Real Numbers as Neverending Trailing Decimal expansions is quite pointless as those numbers can't be written in decimal. Same for some rational decimal expansions. Since you can't split something into 3 parts without a remainder if it is not already a multiple of 3. In decimal, the base isn't a multiple of 3 so if you divide 1 by 3, you should always have a remainder after the division. the unending length of 3s that is commonly used would never equal 1/3 as it would be impossible to write 1/3 using a decimal expansion because there is always a remainder as a result of that division.

>make imageboard to filter midwits
>it's somehow still filled with finitists

>>362
so that must mean finitists aren't midwits.

Why does mathematics have to be limited to the real world? To me this seems to be an underlying assumption for finitists.

>>299
You don't need AC for top though, just always choose the ball that isn't gray like the rest.

Infinites are real but we cannot access their forms directly. We only see the projections on the cave wall :)

>>299
Sorry, I haven't seen that notation for the last equation before, is that supposed to be axiom of infinity? Does y' represent successor? I've seen {y} U y and S(y).

>>709
it is, that notation is definitely nonstandard. Similar notation is y^+

>>710
Thanks
>>299
I mean, if ZFC still works without it, there could be an argument that it isn't 'real'. Could remove Infinity, Replacement, Choice, and I think Foundation.

>>543
Bizarre shit because while infinities aren't tangibly real, finite integers also aren't.

>>299
I have never understood diagonalisation argument.

i never understood why the diagonalization argument doesnt work with the natural numbers
you could consider all natural numbers to be sequences starting with the least significant digit
and then construct a sequence that differs along the diagonal and this sequence must be unique by construction

>>759
The problem is that one would need to restrict to eventually zero sequences, the sequence you'd construct however wouldn't be eventually zero.

>>712
Your post made me realize that being able to conceptualize abstractions that don't actually exist is what we learn to do as toddlers; finitists are essentially just stuck on the adult version of this leap. That's pretty funny.

>>604
Hello

>>299
ggggggggggg

>>299
Claim:
Proof: We use induction. The base case is trivial . Next we introduce notation that \[0.9_n = 0.9999... n times].
Now the inductive step: we assume . Then trivially . It might help to notice
This implies that

>>779
Somebody please counter this

>>779
>>792
If it is defined

Than
but so
Note that , because so

>>793
Does not counters >>779. I don't want a new proof that 0.999.. = 1 , I want to see what is the problem with the above disproff

>>794
But my proof is false
Good luck!

>>779
this argument just shows that a for any natural number n. Since for any n, the last line does not follow.

>>796
How?

>>365
infinitism is a kike lie anyway

>>299

>>779
It's been two months since I posted this. Not a single counter plasible counter argument

>>880
All you've shown is that 1-10^-n is not 1 for all positive whole n, you've not shown it for n=\infty.

>>880
i mean its really quite obvious philoshopically
a thing is defined by its relations, if x+1 = 3, x=2 because we have shown that x has the same properties as 2
1-1/10^inf has the exact same properties as one outside of indeterminate cases

>everything le fake because... it just is ok?

>>902
Disprove this >>779

>>903
I already did in >>882.

>>904
>>882
>all positive whole n
>which goes upto infinity
>but you've not proved that
>because I say so

>>905
You've not proved that because induction doesn't work that way.

>>906
Then teach me how does induction work?

>>907
We start with a foot. Your prove your statement with n.
Then, you show that, if the statement is valid with n, then it will still valid with n+1.
For the last point, you use the induction.

For instance, for any given triple (x,y,z), there is a order x<y<z.

>>907
The reply >>908 wasn't me. The way I'd explain induction is the following:

Take a lineary ordered set L.

A subset I of L is called inductive whenever it satisfies all of the following:
a) It contains all elements less than or equal to some l in L;
b) Given an element j in I, it is greater than or equal to all elements of L or there is some element j' above j in L with [j,j'] in I;
c) If [a,b) is in I, then b is in I.

Induction is the theorem that if L is nonvoid and suprema of bounded above subsets of it exist, then the only inductive subset of L is L itself.

Taking L as the natural numbers, this implies that given a subset of the naturals that contains 0 and contains the successor to any of its elements, that this set contains all of the natural numbers.

Taking your subset of the naturals to be the set of all naturals with a given property, this shows how to check properties for all of the natural numbers, what is known as induction classically.

Replacing the naturals with an ordinal, you obtain what is known as transfinite induction.

>>909
And how does this definition show this >>882.
How would you differ ALL positive whole n from n = \infty

>>910
Because they're different

>>911
>how does this definition show >>882
No response
>how would you differ the two >>910
One liners that conveys nothing?
Is thos ehat you've got. Where is the mathematical spirit?

>>912
I can't figure out if you're criticizing the person arguing for the argument that allegedly shows that 0.99...=1, or the person arguing against it.

>>913
I am the same person who showed .

>>914
Oh, I see now.

As you've checked what I described for taking L the positive integers, you've checked things in accordance with induction as I state in >>882.

The difference between all of the positive integers and infinity is for example their names: "All of the positive integers" is not the same string of symbols as "infinity", one is to justify their equality if one is to claim it. Indeed a further difference is that the former is meant to be a set and the latter is not. This shows their inequality and one cannot show their equality hence.

The reason it's a one liner is as it's straightforward.
You're asking for something similiar as to asking to justify that the natural number 2 and infinity are different. They are different as can be seen by looking at them. Another example is asking why water is different from air, it just is.

>>299
How would you define e with no infinity?

>>949
Why did I not have to solve a captcha?

>>949
Without ever considering the concept of infinity it isn't really feasible. Perhaps as the least positive real e such that x^x<y^y if 1/e<x<y you might like.

Only one thing in the universe is infinite and that's the coping and seething of finitistcels

In order to be mathematics, Ultrafinitist and finitists need to make a logical coherent system.
They can't. It's about the physics to deceide whether the world as a whole is infinite or finite in nature.
As far as I know, our informations doesn't allow such a inference. The topic is closed at this moment.

>>955
I'd say finitism is moreso a philosophical perspective than anything very empirical.